ProofSame.step_le: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_same.bend as ProofSame
Lines 140-148 of lawful-bytes@0.1.1.0/proof_same.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_same.bend&start_line=140&end_line=148

import Base
import lawful-bytes@0.1.1.0/defs.bend as D
import lawful-bytes@0.1.1.0/proof_core.bend as C
import lawful-arrays@0.1.0.0/proof_tree.bend as P

law step_le:
  for +len: U32
  for +t: P.Tree<U32>
  for +d: Nat
  for +s: U32
  for +m: Nat
  for +h: {D.ok(C.BT(len, t), d) == True{} : Bool}
  for +hs: {Nat.is_le(Nat.add(U32.to_nat(s), 1n+m), U32.to_nat(len)) == True{} : Bool}
  {Nat.is_le(Nat.add(U32.to_nat((s + 1 : U32)), m), U32.to_nat(len)) == True{} : Bool}

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_tree.bend&name=Tree
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=ok
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=BT
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_same.bend&name=le_step
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_same.bend&name=step_inc